Arnold Kling  

Banks and Modigliani-Miller

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Greg Mankiw writes,

What about the Modigliani-Miller Theorem? Recall that this famous theorem says that a firm's value as a business enterprise is independent of how it is financed. The debt-equity ratio determines how the risky cash flow from operations is divided among creditors and owners. But it does not affect whether the firm is fundamentally viable as an on-going concern. It seems to me that, as least as first approximation, the logic of this theorem should apply to financial intermediaries as well as other types of business. If not, we need some explanation as to why.

...many banks and other intermediaries now borrow short and lend long. The issue I am wrestling with is whether this maturity transformation is a crucial feature of a successful financial system. The resulting maturity mismatch seems to be a central element of banking panics and financial crises. The open question in my mind is what value it has and whether the benefits of our current highly leveraged financial system exceed the all-too-obvious costs.

Evidently some radiation from Mencius Moldbug has leaked into Harvard Yard.

As readers of this blog know, I have thought about such issues quite a bit. Below are a few points, in case Mankiw or his readers want to catch up.

1. The way I think of Modigliani-Miller is that it creates a world where the structure of financial intermediation does not matter. There are risky projects, and there savers, and the savers have perfect information about the intermediaries' assets and liabillities.

WIth my usual metaphor, think of the risky projects as fruit trees. Think of a financial intermediary, such as a bank, as having an investment in fruit trees that is partly financed by debt and partly financed by equity. Savers can fund fruit trees either directly (without the bank) or by purchasing the debt or equity of the bank. The Modigliani Miller theorem implies that savers will fund the same amount of fruit trees, regardless of what the bank does--in fact, regardless of whether the bank even exists. If the savers want to invest in 100 fruit trees, and they see that the bank has invested in 50 fruit trees, they will invest in 50 fruit trees on their own. If the bank boosts its investment to 80 fruit trees, savers will invest in just 20 fruit trees on their own.

2. Taxes and deposit insurance break the Modigliani-Miller theorem. The corporate income tax rewards banks (and other firms) for leverage, because interest is tax deductible. Deposit insurance rewards leverage, because funding with deposits means that the shareholders get the upside but the taxpayers get the downside. As Russ Roberts has pointed out, it seems to be the de facto policy of the government to bail out other creditors as well, even in cases where it allows shareholders to take a loss. This policy, too, rewards leverage.

3. Bankruptcy costs break the Modigliani-Miller theorem in the other direction. That is, if the only deviation from Modigliani-Miller is that there are deadweight losses (legal fees, loss of brand value) when a firm goes bankrupt, it makes sense to finance entirely with equity.

4. I am afraid that Modigliani-Miller is a really misleading way to think about financial intermediaries, particularly banks. The reality is that savers do not know much about the projects in which the intermediaries invest. In fact, a big function of financial intermediaries is to specialize in knowledge about the projects in which they invest. In this context, debt instruments amount to the bank saying, "Look, you have no idea what my fruit tree portfolio looks like, and you don't want to take a share in the ups and downs of that portfolio. Fine, I'll pay you a fixed interest rate, and the shareholders will deal with the ups and downs of the portfolio."

5. Maturity transformation can, up to a point, work on the basis of diversification. As long as not too many of my long-term investments go bad at once, and as long as not too many of my short-term creditors refuse to roll over my liabilities at once, I can get away with it and make everyone better off than if I did no maturity transformation.

6. As I said in my macro lectures (see number 9), "The nonfinancial sector wants to hold risk-free short-term assets and issue risky long-term liabilities. To accommodate this, the financial sector does the opposite."

As I said in the lectures, the financial sector does this by diversifying more effectively than individuals can and/or by evaluating and managing risks better than individuals can (the intermediary really studies the fruit tree market, while you and I are off doing other things), and, sometimes, by signaling that it is doing such things more than it really is. When banks are signaling that they are sounder than they really are, it can be pretty hard for savers to figure this out. Call this the problem of misleading signals.

7. One fundamental problem in financial regulation is that regulators, too, are often unable to penetrate misleading signals. Often, even the bank's executives believe the misleading signals.

8. A second fundamental problem in financial regulation is that the regulators are also signaling. They are signaling that they are able to protect savers from having to worry about misleading signals from banks. The more that savers believe this, the less vigilant they become in trying to sort out misleading signals. Thus, regulator confidence creates a form of moral hazard. The more that the regulator convinces the public that it has things under control, the less likely that the public will take steps to keep things under control. If you claim that you have made a bank too regulated to fail, the more that the public believes you, the less likely it is that you are going to be able to keep the bank from acting recklessly--and failing.

I do not think that there is a perfect solution to all of this. If you go full-Monty libertarian and take away all government intervention, including deposit insurance, then you have to live with whatever ups and downs occur in people's confidence in bankers' signals. Banks will invest a lot more in signals, and some of that investment will be deadweight loss and some of it will be investment in signals that are downright misleading. On the other hand, if government does intervene, you get deadweight loss from banks trying to game the government. Either way, you get deadweight loss from banks gaming the system. They game the signaling system in a privatized system, and they game the government in a government-regulated system.

I think we have to settle for imperfect financial regulation. Once again, let me make a pitch for policies that make the financial system easy to fix, rather than hoping that we can make it impossible to break.

Comments and Sharing

COMMENTS (8 to date)
Steven writes:

Up to the point where you start to start about misleading signals, everything you say seems to be obviously correct. But then you lose me -- I have no idea what kind of a signaling models you have in mind. Are these separating equilibria, in which case nobody is mislead, but society loses from costly signaling? Or are these pooling equilibria, in which some efficient deals are not made, and other deals are made with inefficient terms? Or do you have in mind behavioral models, in which (some) agents can be deceived, even if each type emits a different signal? Or do you have some non-standard equilibrium concept in mind? Some specific examples of misleading signals might help clarify your argument.

floccina writes:

I think the problem is not failure but a cascade of failures. The problem is feedback. In a better system the weaker players would always be failing but as they fail it would strengthen the remaining players. In the crisis people wanted gov guaranteed assets, if none had existed they would have had to go after real assents which which are the very assets that bank own. Could the problem be that Government assets badly out compete other assets in a crisis.

Milton Recht writes:

The Fisher separation theorem says that the investors (shareholders, depositors) are not concerned with the investment choice opportunities (the fruit trees) of the bank, as long as the bank invests in positive NPV (net present value) projects. Investors choose their own positive NPV investment opportunities for their own funds separate from the bank's investment opportunities.

MM says that the value of the firm, and consequently, the NPV (net present value) of the projects, is independent of the way that the projects and the firm (bank) are financed.

To the extent that a firm can take a tax deduction for interest payments, the deduction is a government subsidy to firms. It allows borrowers to pay, and the lenders to demand, a higher interest rate due to the government subsidy, which by itself should offset the benefit of the tax deduction. If the lender is also taxed on the interest income, then the two taxes will offset each other. If the taxes are equal, then it will be as if there were no interest deduction and if the two taxes are different amounts, a new equilibrium supply and demand point (interest rate cost of borrowing) will occur depending on which tax is higher and by how much. If the two taxes are equal, as they most likely are, the interest deduction will have no effect on leverage. Likewise, if there is only a tax deduction there will be no effect on leverage due to the higher interest rate. It is only when there are different income and deduction tax rates, that there will be some minor leverage effect.

Deposit insurance is a put option (all insurance is a put option) given to the depositor through the bank by the FDIC. Because deposit rates do not risk adjust due to the put, the bank can invest in a greater number of projects with apparent positive NPVs due to low cost deposits. Some of these projects would have a negative NPV if the deposit interest rate adjusted for the riskiness of the project and the bank. The market, however will risk adjust the rate and treat some apparent positive NPV projects as negative NPV projects and decrease the value of the publicly trade stock of the bank.

Deposit insurance fools management, not depositors, as to their available investment projects.

The deposit insurance will have little or no value to the depositor as long as the market value of the assets of the bank is greater than the value of the deposits. The put option will be out of the money. As the market value of the assets declines, due to bad investments, and no longer covers the amount of the deposits, the put option (the FDIC insurance) becomes in the money and increases substantially in value.

Since the bank transfers its assets to the FDIC for the insurance (put) payment of the deposits to the depositors, the FDIC bears all the risk and monetary loss. The FDIC insurance is only paid when deposits exceeds assets. The FDIC pays the full amount of the deposits and loses the excess amount of the deposits over the value of the assets it receives, deposits minus assets.

The essential transparency that is lacking is the value of the FDIC insurance put by institution. However, the publicly traded equity of the bank reflects both the true NPV of the projects on a risk-adjusted cost of financing and reflects the decrease value of the bank due to the value of the put due to the probability of the exercise of the FDIC put and takeover of the bank by the FDIC.

In effect, tax deductions do not increase leverage because it will increase the cost of borrowing and are probability completely offset by the tax on interest income.

Deposit insurance allows banks to invest in otherwise negative risk adjusted NPV projects. While deposit insurance allows banks to invest in unprofitable and negative NPV endeavors, the market price of the asset will be independent of deposit costs or deposit insurance. This is the liquidity funding problem. Banks can have enough funds to invest in a positive NPV valued asset that does not have enough market value to roll over as collateral to fund the asset.

Long-term rates are just the (geometric) average of expected short term rates except for the short-term liquidity premium, and banks will on average just make a small liquidity premium spread. Since long-term rates are just expected averages of short-term rates, half the time the short-term rates will be less then the long-term rates and half the time more than the long-term rate. Half the time, the bank will have a positive interest rate spread and half the time it will have a negative interest rate spread.

Bill Woolsey writes:


I think you assume that dividend and capital gain income is not taxed and that the personal income tax rate on interest is equal to the corporate income tax rate. These are goals of tax reformers, and generally have not been accomplished.

If there is no liquidity premium, then the long rates are averages of short rates. Without the premium, short rates will be higher or lower than long rates half the time.

The first statement, that banks earn the liquidity premium (and pay the costs of maturity transformation) is correct.


I do the MM is useful in a general way. Real investment projects are risky, and capital, leverage, and liquidity transformation are about sharing the risks.

The liquidity risk is that savers help fund projects that take longer to mature than they want to wait to consume. Someone must bear the risk that no other saver will appear to take over the funding. The stockholders of banks that create liquidity bear this risk. But one of the emphasis of MM is that only limited risks are covered by equity and bankruptcy means that debtors bear some risk too. Liquidity creating banks only bear some of the liquidity risk for savers. Businesses could do the same by funding long projects with short bonds.

fundamentalist writes:

"If you go full-Monty libertarian and take away all government intervention, including deposit insurance, then you have to live with whatever ups and downs occur in people's confidence in bankers' signals."

The private insurance industry could easily replace the FDIC. Let people buy insurance on their own deposits if they want. Insurance companies would charge premiums based on the soundness of the bank. In fact, let the bank sell insurance to depositors.

eccdogg writes:

Isn't that essentially what AIG was doing?

Doc Merlin writes:


"Could the problem be that Government assets badly out compete other assets in a crisis."

Yes, I think this is part of it. Governments structure laws to make their assets more competitive, and their ability to freely use violence or threats of stuff to protect the value of their assets increases their value in a crisis.

mark writes:

"In effect, tax deductions do not increase leverage because it will increase the cost of borrowing and are probability completely offset by the tax on interest income"

Don't think so, because many of the largest providers of capital are not taxed - pension funds, endowments and so forth. Many others are pass-through vehicles for tax purposes whose limited partners are such untaxed entities, and the vehicle itself may be a Cayman or other entity that has a lower tax rate and conceivably is exempt from US withholding on the interest payment.

To understand modern corporate finance, it is critical to remember that much of the providers of capital are retirement funds and endowments that are chasing yield and trying to achieve safety at the same time.

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